Please show all necessary work. Thank you. Consider the graph of y = f \'(x) . O

Question

Please show all necessary work. Thank you.

Consider the graph of y = f '(x) . On which intervals will the graph of y = f(x) be increasing? Find the equation of the tangent line to the curve x3 + xy2 =5 at the point (1,2). 5x + 3y = 11 7x + 4y = 15 8x + Sy = 18 9x + 5y = 19 x + 3y = 7 Consider the function = f(x) = 1 / x+ 1 + 1 / x - 1 Choose one of the following: f is concave upwards on (-1,1) f is concave downwards on (-1,1) f is concave upwards on (-1,0) and concave downwards on (0,1) f is concave downwards on (-1,0) and concave upwards on (0,1) Determine the derivative of F(x) = t3dt.

Explanation / Answer

1.) For given graph

We need to use basic rule: A function f(x) is increasing where f'(x)>0

And function is decreasing where f'(x)<0

So, using this rule

Function is increasing in (- infi. , -1) , (0,1)

And function is decreasing in region (-1,0), (1, infinity)

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