WEEK 17

Since we took the two practice AP exams this week, I think I'll just explain some problems off of them.


Number 5: If y = e^2x + tan(2x), then y'(pi) =

first take the derivative: y' = e^2x (2) + sec^2(2x)(2)

Then you plug in pi: 2e^2pi + 2sec(2pi)^2 = 2e^2pi + 2


Number 16: If y = sin^2(5x), dy/dx =

dy/dx = 2 (sin 5x)(cos 5x)(5) <--- take care of exponent, take derivative of sin, take derivative of the inside (5x).

dy/dx = 5 (sin(2 * 5x)) <--- 2sinxcosx = sin2x

dy/dx = 5sin(10x)


Number 18:

remember that f(x) = x
f'(x) = v(x)
f''(x) = a(x)


Number 20: If f(1) = 2 and f'(1) = 5, use the equation of the line tangent to the graph of f at x=1 to approximate f(1.2).

Given: x = 1
y = 2
m = 5
find: x = 1.2

y - 2 = 5 (x - 1)
y - 2 = 5 (1.2 - 1)
y = 3


Number 27:
Always remember that AVERAGE VALUE = INTEGRATION
1/ b-a


Number 28: y = x^2 - 3x. Find y'(1).

y'(x) = 2x - 3
y'(1) = 2(1) - 3
y'(1) = -1
y'(1) = 1


Number 11:
remember that average rate of change = f(b) - f(a) / b - a