Question
Asked Oct 17, 2019
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g(x)=2x^3+5x^2-28x-15

A)find power function

B) homany turning points can this graph have

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Expert Answer

Step 1
(A)
The given function is f(x)= 2x3 + 5x2-28x -15
Definition of the power function:
A power function is of the form of f(x) = k", where k is all real numbers
and n is all real numbers
By the definition of the power function, the given function cannot be written
as the power function
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(A) The given function is f(x)= 2x3 + 5x2-28x -15 Definition of the power function: A power function is of the form of f(x) = k", where k is all real numbers and n is all real numbers By the definition of the power function, the given function cannot be written as the power function

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Step 2
(B)
Find the turning point as follows
Differentiate f(x) = 2x3 + 5x2 - 28x -15 with respect to x
(2x3 +5x2-28x-15)
f'(x)
=6x 10x-28 0
=6x2
10x-28
Equate the derivative to zero to find the critical points.
6x210x 28= 0
-5-193
-5 193
or x
6
6
x 1.4821 or x =-3.1487
Thus, the number of turning points is 2
The turning points of the function f (x)= 2x3 +5x2 -28x -15 are shown in
the given Figure.
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(B) Find the turning point as follows Differentiate f(x) = 2x3 + 5x2 - 28x -15 with respect to x (2x3 +5x2-28x-15) f'(x) =6x 10x-28 0 =6x2 10x-28 Equate the derivative to zero to find the critical points. 6x210x 28= 0 -5-193 -5 193 or x 6 6 x 1.4821 or x =-3.1487 Thus, the number of turning points is 2 The turning points of the function f (x)= 2x3 +5x2 -28x -15 are shown in the given Figure.

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Math

Calculus