Problem : Compute the derivative of f (x) = 6x4 +8x3 +12x2 + 24x.We differentiate term-by-term to get
|f'(x)||=||(4)6x3 + (3)8x2 + (2)12x + 24|
|=||24(x3 + x2 + x + 1)|
Problem : What is the second derivative of g(x) = sin(x)?We have
Problem : Let h(x) = - x2 + 3. For which values of x does h(x) = h'(x)?Since h'(x) = - 2x, we want to solve for x in the equation
|- x2 + 3 = - 2x|
|0 = (x + 1)(x - 3)|
Thus h(x) = h'(x) for x = - 1 and for x = 3.