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Differential Calculus> Image is attached . How to draw graph of ...

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Image is attached . How to draw graph of this function?

Drake , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:

$f(x) = x^{3}+x^{2}+3x+sin(x)$

Domain is given as R.

$f(0) = 0$

function passes through origin.

$f'(x) = 3x^{2}+2x+3+cos(x)$

$f'_{1}(x) = 3x^{2}+2x+3$

$f'_{1}(x) \geq \frac{8}{3}$

$\Rightarrow f'(x) > 0$

So, function is always increasing.

$f''(x) = 6x+2-sin(x)$

From here, find the region where f’’(x) is +ve & -ve.

$f''(x) >0$

-> Concave Up

$f''(x) < 0$

-> Concave down

Thanks & Regards

Jitender Singh

IIT Delhi

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