SOLUTION: please help me with this problem too: Suppose that g is a function such that g'(1) = 0 and g' > 0 when x lies in the interval (-1,1)and g'

SOLUTION: please help me with this problem too: Suppose that g is a function such that g'(1) = 0 and g' > 0 when x lies in the interval (-1,1)and g' < 0 when x lies in the interval (1,3). S

Question 1015662: please help me with this problem too:
Suppose that g is a function such that g'(1) = 0 and g' > 0 when x lies in the interval (-1,1)and g' < 0 when x lies in the interval (1,3). Sketch the shape of g for x values near x = 1. Indicate any special characteristics of g at x =1.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
g must be increasing on (-1,1) and g is decreasing on (1,3). At x = 1, the function g is differentiable, and the slope of the tangent line at x = 1 is 0, so g attains a local maximum.
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