21. Find the indicated quantities for the function y = f(x)= 2x2 +5(a) The change in y if r changes from 1 to 3(b) The average rate of change of y with respect to x if e changes from1 to 3(c) The slope of the secant line through the points (1, f(1)) and (3, f(3))(d) The rate of change of y with respect to x at x =1(e) The slope of the tangent line to the graph of y = f(x) at x 1(f) f'(1)

Question
Asked Oct 17, 2019
21. Find the indicated quantities for the function y = f(x)= 2x2 +5
(a) The change in y if r changes from 1 to 3
(b) The average rate of change of y with respect to x if e changes from
1 to 3
(c) The slope of the secant line through the points (1, f(1)) and (3, f(3))
(d) The rate of change of y with respect to x at x =1
(e) The slope of the tangent line to the graph of y = f(x) at x 1
(f) f'(1)
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21. Find the indicated quantities for the function y = f(x)= 2x2 +5 (a) The change in y if r changes from 1 to 3 (b) The average rate of change of y with respect to x if e changes from 1 to 3 (c) The slope of the secant line through the points (1, f(1)) and (3, f(3)) (d) The rate of change of y with respect to x at x =1 (e) The slope of the tangent line to the graph of y = f(x) at x 1 (f) f'(1)

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Expert Answer

Step 1

Hi, as per our norms, we answer three sub parts to a question. Since your question has six sub parts, we will answer the first three parts. You may post a separate question to ask the remaining sub parts.

Step 2

The change in y:

Substitute the values of x and get the corresponding y. Calculate the difference in values of y to know the change.

y f(x) 2x2+5
for x 1 y f(1) = 2(1)2 +5= 7
for x3, y f(3) 2(3) 5=23
Ay 23-7 16
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y f(x) 2x2+5 for x 1 y f(1) = 2(1)2 +5= 7 for x3, y f(3) 2(3) 5=23 Ay 23-7 16

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Step 3

Average rate of change of y...

Average rate of change
f(b)-f(a)
b-a
f(3)-f(1)
3-1
23-7
2
16
-8
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Average rate of change f(b)-f(a) b-a f(3)-f(1) 3-1 23-7 2 16 -8

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Tagged in

Math

Calculus

Functions