(1, f (1))Sy= f(x)(11, f(11))-XThe figure above shows the graph of the differentiable function f for 1 ≤ x ≤ 11 and the secant line through the points (1, ƒ (1)) and (11, ƒ (11)). For how manyvalues 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?

Instataneous rate of change is given by slope of tangent.and the average rate of change is given by…

Answered: The figure above shows the graph of the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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3 Graph of f' The graph of f', the derivative of the function f, is shown above. On which of the following open intervals is the graph of f concave down? (-5, –3) and (1, 6) (-3,1) and (6, 8) P Type here to search 35°F Chp f2 13 C esc f1 14 D 立

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
The graph of the derivative of f' of a continuous function f is given in Figure 1. y = f'(x) 2- 2 /4 6. |-2 Figure 1 a) On what intervals is f increasing and on what intervals is f decreasing? b) At what value of x does f have a local maximum, and local minimum? c) On what intervals is f concave upward and concave downward? d) State the x-coordinates of the point(s) of inflection.
For the function, S(t)=3-2t^2+t find a) Net change in S on [-4,4] b) Average rate of change of S on [-4,4]

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