Some help would be lovely !!:D
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is
, with x ≠ 2.
A)On what intervals is the graph of g concave down? Justify your answer
B)Write an equation for the tangent line to the graph of g at the point where x = 3.
Stacey Warren - Expert brainly.com
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yep yep did that got plus or minus 4 for g'(x)
If you complete the square for the numerator, you get this
x^2 - 4x + 16
x^2 - 4x + 4 - 4 + 16
(x^2 - 4x + 4) + 12
(x-2)^2 + 12
So this means that x^2 - 4x + 16 is always positive. The same applies to (x-2)^2. Overall, g '' (x) is always positive
since g '' (x) is never negative, it's impossible for g to be concave down
okay so if g''(x) is positive then g(x) is concave up?
yeah g is concave up over all of g's domain
okay and as far as i can get on part b is getting the slope ... wich is -7
so now i need a point on the tangent line right?
g(3) = 4 which means (3,4) lies on the g(x) function
m = -7
x = 3
y = 4
with y = mx+b and solve for b