Suppose that g(x) is a function that is defined and differentiable for all real numbers x and that g(x) has the following properties:

Question

(i) g(0)=5 and g'(0)=-5/6 .
(ii) g(7)=6 and g'(7)=6 .
(iii) g(x) is concave up for x<7 and concave down for x>7.
(iv) g(x)>_-15 for all x.

Use these properties to answer the following questions.
(a) How many zeros does g have?
(b) How many zeros does g' have?

Answer 1

sorry - once is enough. But
(iii) says that g''(7) = 0
so start with g'' = a(x-7) with a < 0
(iv) says that there will be either 1 or 3 zeroes (why?)

Now you try something.