please please answer 13 a and b show steps If gx x2 3x 10

please please answer 1.3 a and b

show steps

If g(x) = -x^2 + 3x + 10, find g(2),g(t^2),g(3x-2)Give the domain, range, and intercepts for the graphed function: Find for the faction 1.2 a. above. Give the intervals where the graphed function is increasing and decreasing. Also give any relative maximum or relative minimum points.

Solution

13a) g(x) = -x² + 3x + 10

g(h +1) = -(h +1)² + 3(h +1) + 10 = -(h² + 2h + 1) + 3h + 3 + 10

==> g(h +1) = -h² - 2h -1 + 3h + 13

==> g(h +1) = -h² + h + 12

g(1) = -1² + 3(1) + 10 = 12

[g(h +1) - g(1)]/h = [-h² + h + 12 - 12]/h

==> [-h² + h ]/h ==> -h + 1

b) function is increasing in the interval (-4 , -2) U (3.5 , 5)

function is decreasing in the interval (-2 , 3.5) U (5 , infinity)

local maximums at (-2 , 4) and (5 , -2)

local minimum at (3.5 , -5)

Global maximum at (-2 , 4)