One Question involving the definition of the derivative of a function Use the de

Question

One Question involving the definition of the derivative of a function Use the definition of the derivative to find the derivative of the following function f (x) = X^2 - 4x + 5 One multi-part question to test basic differentiation rules Use an appropriate differentiation role to find the derivative of the following F(x) = 4x^3 - 5x^2 + 6x - 7 F(x)=sin(x^2) One qestion involving the equation of a tangent line Find the slope intercept form of the equation of the tangent line to the function F(x) = X^3 + 1 at x =2. Sketch the graph of the function and the tangent line. One question involving the finding of the maximum and minimum values of a function on a dosed interval A) Find the maximum and minimum values of f(x)= x^3 - x on the interval [-1,1] Find the dimensions of the rectangle with the largest possible area that has perimeter 50. Sketch &e; graph of F(x) = x^3 + 6x^2 + 9x + 1 Use implicit differentiation to find dy/dx for the following Two straight roads intersect at right angles. At 10AM a car passes through the intersection headed due East at 30mi/h. At 11AM a truck heading due north at 40 miA intersection. Assume that the two vehicles maintain the given speeds and directions. At what rate are they separating at 1PM.

Explanation / Answer

1)F(x)=x2 -4x+5

F(x+h)=(x+h)2 -4(x+h)+5

F(x+h)=x2+2xh+h2-4x-4h+5

derivative F '(x)=limh->0 [F(x+h) -F(x)]/h

F '(x)=limh->0 [(x2+2xh+h2-4x-4h+5) -(x2 -4x+5)]/h

F '(x)=limh->0 [2xh+h2-4h ]/h

F '(x)=limh->0 2x+h-4

F '(x)=2x+0-4

F '(x)=2x-4

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