Question

1.Using only definition of a derivative compute f'(2) for f(x)=1/x

2 Find all points on the curve y=x^3/3 +x2/2 where the tangent line is horizontal. Any vertical tangent lines?

b. Find an equation of the line tangent to the curve at x=1

c. Find linear approximation L(x) of the curve at x=1

3.find the derivative of 7x/cos(pi x)

Answer 1

for the first one compute
\[\lim_{x\to 2}\frac{\frac{1}{x}-\frac{1}{2}}{x-2}\]

Answer 2

for the second one, take the derivative set it equal to zero and solve