Calculus

Derivatives

Instantaneous Rate of Change

         

Let f(x)=6x2+7x5f(x)=6 x^2+7x-5. Then if the average rate of change of f(x)f(x) when xx changes from 00 to 1818 is the same as the rate of change of f(x)f(x) at x=ax=a, what is the value of aa?

What is the rate of change of y=x(x5)2(x+3)3 y = \frac{x(x-5)^2}{(x+3)^3} at x=1 x = 1 ?

For a function f(x)=x2+px+qf(x)= x^2+px+q, if the average rate of change of f(x)f(x) when xx changes from aa to bb is the same as the rate of change at x=cx=c, what is the value of cc?

A person 180180 cm tall walks away from the base of a streetlight 44 m high. If she follows a straight line at a velocity of 121121 m/min, what is the rate of change of the length of her shadow (in m/min)?

What is the rate of change of the function y=ln(8x) y = \ln ( 8 x) when x=116 x = \frac{ 1}{16} ?

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