Given that the point (4,10) is a max on the quadratic function, explain whether these statements are true or false: a. the instantaneous rate of change at 4 is 0 b. f(6)> f(4) d. there is only one possible value for x that has an instantaneous rate of change = 0.

(a) TRUE; (b) FALSE; (c) TRUE

Step-by-step explanation:

a. The instantaneous rate of change at 4 is 0.  TRUE.  

The function is f(x) = a(x-4)^2 - 10; the derivative of this function is f '(x) = 2a(x-4), which must equal zero (0) at the vertex / max (4,10).  Zero slope at the vertex corresponds with instantaneous rate of change zero at that point.

b.  f(6)>f(4).  FALSE.

Using the function given in (a), above, f(x) = a(x-4)^2 - 10.  Since (4,10) is the max of this function, f is increasing on (-infinity, 4) and decreasing on (4, infinity).  Thus, f(6) is smaller than f(4).  

c. There is only one possible value for x that has an instantaneous rate of change = 0.  TRUE

The inst. rate of change takes on the value 0 only at (4,10), since (4,10) is the vertex of this downward-opening parabolic graph.

e

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)