Question

Find the relative extrema, if any, classify as absolute max/min.

a.) f(x)= x+1/x-2 on [2,4]

b.) f(x)= x^(2) -2x-3 on [-2,3]

c.) f(x)= x^(2/3) (x^2-4) on [-1,3]

Solve for x:

a.) 6^(2x) =36

b.) 2^(2x) -4 * 2^(x) +4=0

c.) 3^(x-x^2) =1/9x

Determine if the following statements are true or false. If it is true, explain why. If it is false, provide an example.

a.) If a and b are positive numbers, then (a+b)^x=a^x+b^x

b.) If x < y, then e^x < e^y

c.) If 0 < b <1 and x < y then b^x > b^y

d.) if e^kx > 1, then k > 0 and x >0

Answer 1

Finding relative extrema,checking whether they are  absolute maxima/ minima .Also solving indicial equation.