AP Calculus AB Exam Review UPDATED ACTUAL QUESTIONS AND CORRECT
ANSWERS
Average Rate of Change of f(x) on [a,b]
, Instantaneous Rate of Change at x=a
If f(x) is increasing, then f'(x) is? f'(x) > 0 (positive)
If f(x) is decreasing, then f'(x) is? f'(x) < 0 (negative)
If f(x) is concave up, then f''(x) is? f''(x) > 0 (positive)
If f(x) is concave down, then f''(x) is? f''(x) < 0 (negative)
If f'(x) is increasing, then f''(x) is? f''(x) > 0 (positive)
If f'(x) is decreasing, then f''(x) is? f''(x) < 0 (negative)
Equation for the line tangent to f(x) at x=a
Slope of the line tangent to f(x) at x=a f'(a)
A tangent line approximation is an "underestimate" when f is concave up (f''>0)
A tangent line approximation is an "overestimate" when f is concave down (f''<0)
Differentials 1. Find f'(x)
2. Let dy=f'(x)*dx
A function is continuous if and only if; (aka "The Definition
of Continuity")
If a function is "differentiable" then, It is also continuous
Derivative of a constant
Derivative of kx
ANSWERS
Average Rate of Change of f(x) on [a,b]
, Instantaneous Rate of Change at x=a
If f(x) is increasing, then f'(x) is? f'(x) > 0 (positive)
If f(x) is decreasing, then f'(x) is? f'(x) < 0 (negative)
If f(x) is concave up, then f''(x) is? f''(x) > 0 (positive)
If f(x) is concave down, then f''(x) is? f''(x) < 0 (negative)
If f'(x) is increasing, then f''(x) is? f''(x) > 0 (positive)
If f'(x) is decreasing, then f''(x) is? f''(x) < 0 (negative)
Equation for the line tangent to f(x) at x=a
Slope of the line tangent to f(x) at x=a f'(a)
A tangent line approximation is an "underestimate" when f is concave up (f''>0)
A tangent line approximation is an "overestimate" when f is concave down (f''<0)
Differentials 1. Find f'(x)
2. Let dy=f'(x)*dx
A function is continuous if and only if; (aka "The Definition
of Continuity")
If a function is "differentiable" then, It is also continuous
Derivative of a constant
Derivative of kx
