# Graphical Analysis

• Oct 31st 2009, 10:12 AM
Tokyotower
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
• Nov 1st 2009, 01:40 AM
CaptainBlack
Quote:

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?

$f(0)=0$ and $\lim_{x \to 0_-} f'(x)= +\infty$ and $\lim_{x \to 0_+} f'(x)= +\infty$ should tell you that the curve has a cusp at $x=0$.

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

CB