Question

Calculus Question
I am given tables and ask which of the following could be a table of values of g

Answer 1

So basically I am told that the function g(x) is continuous on the closed interval [-2,0] and twice differentiable on the open interval (-2,0).

Answer 2

If g'(-1)=-2 and g"(x)>0 on the open interval (-2,0), which of the following could be a table of values of g?

Answer 3

g"(x)>0 means concave up on interval (-2,0)
I gotta go pick up my child from school. I will be back soon..........

Answer 4

but I appreciate any and all help from anyone......

Answer 5

g''(x) > 0 means the slope of tangent line is increasing

Answer 6

the curve may look something like above ^

Answer 7

we can eliminate A as the first differences are constant - that means slope is constant - but we want a table whose slope is increasing !

Answer 8

there is one more table with constant slope which we can eliminate right away...

Answer 9

ok I am back

Answer 10

welcome back !

Answer 11

so am I learning this incorrect, I thought when the second derivative is positive that meant that the f(X) is concave up

Answer 12

is it best for me to plot them all out

Answer 13

`concave up` and ` increasing slopes ` are equivalent statemetns