How do you find the points where the graph of

Ben Mcdonald

Ben Mcdonald

Answered question

2022-02-10

How do you find the points where the graph of the function y=2x(8x)5 has horizontal tangents?

Answer & Explanation

anthonystb5

anthonystb5

Beginner2022-02-11Added 11 answers

Explanation:
Compute the first derivative:
y=163x8x
Set that equal to zero:
163x8x=0
x=163
y(163)=2(163)(8163)0.5
The horizontal tangent is at (163,(643)23)
liofila3w7

liofila3w7

Beginner2022-02-12Added 13 answers

For the horizontal tgts., the slope of tgt., or, what is the same as to
say, dydx, must be 0.
dydx=0ddx{2x(8x)12}=0
2{xddx8x+8xddx(x)}=0
8x=x28x
2(8x)=xx=163
When, x=163,y=2(163),y=2(163)8163=323223=64323
It follows that, the curve C:y=2x(8x)0.5 has a horozontal
tangent at the pt. (163,64323)

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