The figure above shows the graph of the differentiable function f for 1 ≤ x ≤ 11 and the secant line through the points (1, f (1)) and (11, f (11)). For how many values of x in the closed interval [1, 11] does the instantaneous rate of change of fat x equal the average rate of change of f over that interval?

4 For the function f(x) evaluate and simplify the Difference Quotient. SHOW ALL WORK. a) Solution: Difference Quotient = b) Use the difference quotient to find the average rate of change of the function f(x) over the interval (3, 3 + h), where h = 1: slope of secant line ; {Give at least 4 decimal places} and also h .1: slope of secant line %3D . {Give at least 4 decimal places} Sketch each of these situations in your Notebooks. c) What value of h will produce a secant line with a slope of -0.4443 over the interval from 3, 3 + h? h {Give at least 4 decimal places when needed.}

Let f be a differentiable function. We are given the following values of f and f': x|ƒ(x) | ƒ'(x) 7 Consider the functions g, h, k defined by Find the following values: a) g' (4) = b) h' (4) = c) k'(4) = g(x) h(x) k(x) 4 16 36 = = = 36 2 3 -3 4 f(x²) fof(x) 3(f(x))³ — 1(ƒ(x))²

On the interval x∈(1,2), the curve y=x^3−6x^2+9x+1 is. decreasing and concave down horizontal increasing and concave down decreasing and concave up increasing and concave up