1. ## Graphical Analysis

I need some help with these 2 questions, thank you

a) For this case, sketch the graph of a continuous function f(x) such that
f(0)=0, f"(x)>0 for x<0, f"(x)< 0 for x>o, lim f'(x)= +infinity (x approaches 0-) and lim f'(x)= +infinity (appraches 0+)
what would the graph look like?

b) For what real number values of 'p' does the equation
p= 3x-9 have 2 real solutions (algebraically)
x2-x-2

2. Originally Posted by Tokyotower
I need some help with these 2 questions, thank you

a) For this case, sketch the graph of a continuous function f(x) such that
f(0)=0, f"(x)>0 for x<0, f"(x)< 0 for x>o, lim f'(x)= +infinity (x approaches 0-) and lim f'(x)= +infinity (appraches 0+)
what would the graph look like?
$\displaystyle f(0)=0$ and $\displaystyle \lim_{x \to 0_-} f'(x)= +\infty$ and $\displaystyle \lim_{x \to 0_+} f'(x)= +\infty$ should tell you that the curve has a cusp at $\displaystyle x=0$.

The other conditions tell you that the slope is increasing when $\displaystyle x$ is negative and decreasing when $\displaystyle x$ is positive.

CB