SOLUTION: Let f\left(x\right)=\frac{5}{2}x^2-e^x . Find the value of x for which the second derivative f^{\:ii}\left(x\right) equals zero.

Algebra ->  Sequences-and-series -> SOLUTION: Let f\left(x\right)=\frac{5}{2}x^2-e^x . Find the value of x for which the second derivative f^{\:ii}\left(x\right) equals zero.      Log On


   

Question 1183580: Let f\left(x\right)=\frac{5}{2}x^2-e^x . Find the value of x for which the second derivative f^{\:ii}\left(x\right) equals zero.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let f%28x%29=%285%2F2%29x%5E2-e%5Ex .
Find the value of x for which the second derivative f''%28x+%29 equals zero.
f%28x%29=%285%2F2%29x%5E2-e%5Ex+....first find first derivate
f ‘%28x%29=+5x+-+e%5Ex
now find second derivate
f‘‘%28x%29=+5+-+e%5Ex

second derivative f''%28x+%29 equals zero:
5+-+e%5Ex=0
5+=e%5Ex..........take natural log of both sides
ln%28e%5Ex%29=ln%285%29
x%2Aln%28e%29=ln%285%29............ln%28e%29=1
x=ln%285%29