#### To determine

**To find:** The value of *c* where the curve have inflection points.

#### Answer

−ex6x.

#### Explanation

**Given:**

The expressionis y=cx3+ex

**Formulae used:**

The derivative formula

Consider y=cx3+ex

Inflection point is where the second derivative of the curve vanishes that is y″=0

y=cx3+exy′=3cx2+exy″=6cx+ex

Put y″=0 to get the value of *c*

y″=6cx+ex6cx+ex=0c=−ex6x

The range of function y=cx3+ex

Roots of the this function are

x=−6x=6

Hence range of this function will be

{y∈R:3ey≤(7−1)e7}

In domain {x∈R:x≠0}.

**Conclusion: **Hence the value of *c* for which the curve y=cx3+ex have inflection point is −ex6x. The range of function is {y∈R:3ey≤(7−1)e7} in domain,{x∈R:x≠0}.