`f(x) = e^x - 0.186x^4` Produce graphs of `f` that reveal all the important aspects of the curve. In particular, you should use graphs of `f'` and `f''`

Textbook Question

Chapter 4, 4.6 - Problem 8 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`f(x)=e^x-0.186x^4`

`f'(x)=e^x-0.186(4x^3)`

`f'(x)=e^x-0.744x^3`

`f''(x)=e^x-0.744(3x^2)`

`f''(x)=e^x-2.232x^2`

Refer the attached graph in image and link. f(x) plotted in red color,f'(x) in blue color and f''(x) in green color.

From the graph,

Local Maximum `~~` 5 at x `~~` 2.975

Local Minimum `~~` 5 at x `~~` 3.025

Inflection points at x `~~` -0.5 ,x `~~` 1.25 ,x `~~` 3.0

The function is Concave up in the intervals about (-0.5,1.25) and (3,`oo` )

The function is Concave down in the intervals about (-`oo` ,-0.5) and (1.25,3)

 

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