Its just for question 29 (a) Find the average rate of change of P as Vin that, f

Question

Its just for question 29

(a) Find the average rate of change of P as Vin that, form 200 in^3 to 250 in^3. (b) Express V as a function of P and show that the instantaneous rate of change of V with respect to P is inversely proportional to the square of P. For the function f whose graph is shown, arrange the following numbers in increasing order: 0 1 f'(2) f'(3) f'(5) f"(5) (a) Use the definition of a derivative to find f'(2), where f(x) = x^3 - 2x. (b) Find an equation of the tangent line to the curve y = x^3 - 2x at the point(2, 4). (c) Illustrate part (b) by graphing the curve and the tangent line on the same screen. (a) If f(x) = e^-x^2, estimate the value of f'(1) graphically and numerically. (b) Find an approximate equation of the tangent line to the curve y = e^-x^2 at the point where x = 1.

Explanation / Answer

f ''(5) < 0< f ' (2) < 1 < f '(5) < f'(3).

the reason being is that at x=5, the curve is downwards,this happens when double derivative is negative,so this will be lesser of all. now, as the slope of curve increases, the value of tan(theta) increases because tan (theta) is increasing function in (0,pi/2).

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