# How do you sketch the graph that satisfies f'(x)>0 when x does not equal 2, f(2)=1?

##### 2 Answers

Since the derivative is greater than

A perfect example of this would be the cubic function

Hopefully this helps!

I would apologize for being pedantic, but this is an educational website.

#### Explanation:

The question does not give any information about

It is important to understand the use of language and logic in mathematics.

Saying

So,

(1) Any line with positive slope through

for example

graph{y-1=3(x-2) [-1.907, 9.19, -2.45, 3.1]}

Replace

Any other curve with positive slope everywhere will also work, for example

graph{e^(x-2) [-1.29, 8.574, -2.14, 2.793]}

(2) We could also have a piecewise function with positive slope except at a discontinuity at

This has

Or

graph{(x-2)^(1/3)+1 [-2.68, 5.113, -0.86, 3.037]}

(3) Or we could have a translation of an odd power function.

These have

graph{(x-2)^(7/3)+1 [-1.216, 3.65, -0.128, 2.305]}