Question
Asked Jan 17, 2020
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Sketch the graph of a differentiable function y = ƒ(x) through the point (1, 1) if ƒ′(1) = 0 and

a. ƒ′(x) > 0 for x < 1 and ƒ′(x) < 0 for x > 1;

b. ƒ′(x) < 0 for x < 1 and ƒ′(x) > 0 for x > 1;

c. ƒ′(x) >0 for x ≠ 1;

d. ƒ′(x) < 0 for x ≠ 1.

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Expert Answer

Step 1

We need to Sketch the graph of a differentiable function y = ƒ(x) through the point (1, 1) if ƒ′(1) = 0 and

(a)  ƒ′(x) > 0 for x < 1 and ƒ′(x) < 0 for x > 1;

i.e.; the function is increasing for x < 1 and the function is decreasing for x > 1.

Also, the function is passing through (1, 1) and ƒ′(1) = 0 (means the function must be having a local maxima or minima at x = 1.).

So, the graph can be

Calculus homework question answer, step 1, image 1
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Step 2

(b)

ƒ′(x) < 0 for x < 1 and ƒ′(x) > 0 for x > 1;

i.e.; the function is decreasing for x < 1 and the function is increasing for x > 1.

Also, the function is passing through (1, 1) and ƒ′(1) = 0 (means the function must be having a local maxima or minima at x = 1.).

So, the graph can be

Calculus homework question answer, step 2, image 1
fullscreen
Step 3

(c)

ƒ′(x) >0 for x ≠ 1;

i.e.; the function is increasing for x ≠ 1.

Also, the function is passing through (1, 1) and &...

Calculus homework question answer, step 3, image 1
fullscreen

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Tagged in

Math

Calculus

Derivative