Question

In Problem, determine whether f is continuous at c.

$f\left(x\right)=3x^4-x^2+2,c=5$

Short answer

The given polynomial function is $f\left(x\right)=3x^4-x^2+2$continuous at c = 5

Step-by-step solution

Step1. Given information 

Polynomial function $f\left(x\right)=3x^4-x^2+2$

c=5

We know that

A function is called continuous function when at x= a,

localid="1647106984859" $\underset{x\to a}{lim}f\left(x\right)=f\left(a\right)$

and defined for every number of domain

Step2. Calculations of continuity

$$\begin{gathered} \underset{x\to 5}{lim}f\left(x\right)=f\left(5\right) \\ =3{\left(5\right)}^4-{\left(5\right)}^2+2 \\ =1875-25+2 \\ =1852 \end{gathered}$$

as $\underset{x\to 5}{lim}f\left(x\right)=f\left(5\right)$

so the polynomial function is continuous at c= 5