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On what interval/s is the following function increasing? f(x)=4x^3-5x^2-7x?

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On what interval/s is the following function increasing? f(x)=4x^3-5x^2-7x?

I think the answer is (1/12 15.44,,∞).
asked Feb 9, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The function is image.

Differentiate with respect to image.

image

Find the critical number by equating image to zero.

image

Roots of the quadratic equation image are  image.

Compare image  with image.

Substitute corresponding values in the image

image

image

image.

Step 2:

Critical points are image.

Test intervals are image.

The function is increasing on the interval image and image

and decreasing on the interval image.

Solution:

The function image is increasing on intervals image and image.

answered Feb 9, 2015 by cameron Mentor

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