Question

The graph of the function $f\left(x\right)=2x^3-7$ goes :

• A. up to the right and down to the left
• B. down to the right and up to the left
• C. up to the right and up to the left
• D. down to the right and down to the left
• E. none of these ways.

Answer 1

The correct option is A up to the right and down to the left

Given $f\left(x\right)=2x^3-7$

$\Rightarrow f^{{}^{\prime }}\left(x\right)=6x^2>0\Rightarrow$ strictly increasing function

$\therefore$Function is strictly increasing function

And $f\left(0\right)=0$ when $x=\sqrt[3]{3\frac{7}{2}}$

$\Rightarrow$Graph will go to infinity to the right as $x\to \infty$

$\Rightarrow$Graph will go to minus infinity to the left as $x\to -\infty$

$\therefore$Graph goes up to the right and down to the left

Option 'A' is correct