Question
plz explane how we get the answer
For the function f (x) graphed below, find the following Find the derivative for each of the following functions. In this problem you must show all steps. Output from at TI89 calculator is not acceptable and will receive no credit. Given that f (2) = 3, f' (2) = -1, answer the following: If g(x) = f(x) In x Find an expression for g '(x). Evaluate g'(2). If h(x) = In( f (x)) Find an expression for h '(x). Evaluate h'(2). For the function f(x) = In(2x+3): Find the linearization for f at x = -1. Use the linearization to approximate In(l.25). Is the approximation in part b) an overestimate or an underestimate? Explain why. A stone is thrown straight up from the edge of a roof, 650 feet above the ground, at an initial speed of 12 feet per second. The acceleration due to gravity is -32 feet per second. Find the formula for v(t), the velocity of the stone t seconds after its release. Find the formula for h(t), the height of the stone above the ground t seconds after its release. What is the highest height can the stone reach? At what time does the stone hit the ground? How fast is it going when it hits the ground? Given the function f (x) = ax3 - x4 where the constant a is a positive parameter. Find the x-intercept and y-intercept. State x and y coordinates. Your answer may contain the parameter a. Find the critical point(s) of f (x). State x and y coordinates. Your answer may contain the parameter a. Check if these critical points are local max or min. Find the inflection point(s) of f (x). State x and y coordinates. Your answer may contain the parameter a. Sketch a representative graph of f (x) labeling the points found in (a) and (c). The graph below represents the velocity of a bicyclist. X is given in hours and Y is given in miles per hour. Suppose she started riding from her house. How far from her house was she after three hours. Find the total distance she rode in three hours. Find the farthest she was from her house. Give an interval where her acceleration was negative but her velocity was positive. Suppose that a volcano is erupting and readings of the rate r(t) at which material is spewed into the atmosphere are given in the following table. Time is measured in seconds and r(t) is measured in metric tons per second. Write an integral that represents the amount of material ejected into the atmosphere over the 6 second period. Estimate your integral using 3 right rectangles. Is the estimate too big or too small? Explain your answer. Give an estimate using 3 midpoint rectangles. For the function f (x) = x2, Write an integral to represent the area under it and above x-axis from x=0 to x=8. Estimate your integral with 4 rectangles using left endpoints. Is your estimate an overestimate or an underestimate? Explain by sketching the graph. Estimate your integral with 4 rectangles using midpoints. A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minutes after the woman starts walking? Find the point on the line 2x + 6y = 4 which is closest to the point (4, 6). A car braked with a constant deceleration of 16 ft/s2, producing skid marks measuring 200 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?
Explanation / Answer
a far from house = displacement(sign chnange included) = area under the graph = 0.5*1*10 + 1*10 +0.5*0.5*10 + 0.5*0.5*(-10) = 5 +10+2.5-2.5 = 15 miles b distance from home she rode in 3 hrs = sum of all areas = 5 +10 + 2.5 +2.5 (note : for distance we do not take the negative sign of velocity) = 20 miles c she was farthest at t = 2.5 hrs ie at a displacement of 5+10+2.5 = 17.5 miles from home . d the slope of in the graph gives the acceleration , as we can see slope is negative from t = 2 till t= 3 hrs but the velocity was positive with negative slope from 2 to 2.5 hrs ans: for d part is from 2 to 2.5 hrs
