Minimize It!

Calculus Level 1

What is the minimum value of $f(x) = 10{e}^x-10ex+8 ?$

6 8 10 12

1 solution

Matthew Riedman
Apr 20, 2016

Taking the derivative, $\frac{d}{dx}\left(10e^x-10e+8\right)=10e^x-10e$ We are looking for when the derivative is 0: $10e^x-10e=0$

$10e^x=10e$

$e^x=e$

$x=1$

Plugging x back in, the minimum is $10e^1-10e\cdot 1+8=\boxed{8}$

But what is the proof of at x = 1 minimum value occurs?

Rajan Saha Raju - 1 year, 7 months ago

I believe because the 2nd derivative is 10e^x, which is positive. Therefore x=1 was a min., not a max.

Tony Miller - 1 year, 6 months ago

Gooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooood

Sushanth S - 10 months, 2 weeks ago