Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = ln(x2 + 5x + 13), [−3, 1]

Question

Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = ln(x2 + 5x + 13),    [−3, 1]

ganeshie8 · Answer

what have u tried

mathmale · Answer

Important:  Note that the domain of the ln function is "all real numbers greater than zero."  Thus, you must determine whether the input to the ln function in this particular problem (x^2 + 5x + 13) is greater than zero on the interval [-3,1].  Can you do that?  In your shoes, I'd graph that quadratic function on that interval.

anonymous · Answer

i know you have to find the derivative but I'm confused on what to do after

mathmale · Answer

You may ... or may not ... need to find the derivative.  Generally, in an absolute minimum / absolute maximum problem you evaluate the function at the endpoints of the interval, as well as find the derivative of that function, set that derivative = to 0 to determine any critical values, and then evaluate the given function at any such critical values that lie within the given interval (which in this case is [-3,1].

anonymous · Answer

so then what would the absolute min and max be?

mathmale · Answer

Have you evaluated x^2 + 5x + 13 at the endpoints of [-3,1]?
Have you applied the chain rule to differentiate ln (x^2 + 5x + 13) ?

mathmale · Answer

I'd be happy to help you with that question, but would like for you to follow these suggestions in order first, if you don't mind.  We'll need to evaluate  ln (x^2 + 5x + 13) at the endpoints of the given interval.  We'll need to find any critical values that happen to lie within the given interval, and then evaluate  ln (x^2 + 5x + 13) at any such c. value.

mathmale · Answer

Just supposing that you find you have two c. v. within the given interval, then you'd be evaluating  ln (x^2 + 5x + 13) for four different x values.

mathmale · Answer

What is the first derivative of  ln (x^2 + 5x + 13) ?