Solve the following:
1. Find the rate of change dy/dx where x = x0 (Compute the derivative of the function from the definition only, using limits. Show all steps.)
y = 1/(2-x), x0 = -3
2. Differentiate the function. Simplify your answer.
f(x) = (1/4)x^8 - (1/2)x^6 - x +2
3. Find dy/dx by implicit differentiation.
y^2 +3xy -4x^2 = 9
4. Determine the critical numbers for the given function and classify each critical point as a relative maximum, a relative minimum, or neither.
f(t) = 10t^6 +24t^5 +15t^4 +3
5. Compute the elasticity of demand for the given demand function D(p) and determine whether the demand is elastic, inelastic, or of unit elasticity at the indicated price p.
D(p) = sqrt(400 - 0.01p^2) , p = 120
6. Differentiate the function:
f(t) = [ t^2 +2t +1]/[t2+3t -1]
7. Differentiate the function and simplify your answer.
f(x) = sqrt(5x^6 -12)