AP Cal Chapter 3 Exam 2025 With
100% Correct Answers
Use the definition of f'(a)=lim h->0 of (f(a+h)-f(a))/(h) to find the derivative of the given function
at the indicated point
f(x)= 22-10x, a=1 - CORRECT ANSWER✔✔-10
Use the definition of f'(a)=lim h->0 of (f(a+h)-f(a))/(h) to find the derivative of the given function
at the indicated point
f(x)= x^3+7, a=4 - CORRECT ANSWER✔✔48
Use the definition of f'(a)=lim x->a of (f(x)-f(a))/(x-a) to find the derivative of the given function
at the indicated point
f(x)= √x, a=36 - CORRECT ANSWER✔✔1/12
Use the definition of f'(a)=lim x->a of (f(x)-f(a))/(x-a) to find the derivative of the given function
at the indicated point
f(x)= 4-x^2, a=8 - CORRECT ANSWER✔✔-16
Find dy/dx if y=17-4x - CORRECT ANSWER✔✔-4
Find d/dx(3x^2-2) - CORRECT ANSWER✔✔6x
, Find f'(x) if f(x)=8x-12 - CORRECT ANSWER✔✔8
Find an equation of the tangent line to the graph of y=x^2-x, at the point (3,6) - CORRECT
ANSWER✔✔y=5x-9
Find an equation of the tangent line to the graph of y=10√x-x+7 at the point (100,7) - CORRECT
ANSWER✔✔y-7=-1/2(x-100)
Find the equation of the normal line to the curve y=2x+4x^2 at the point (-5,90) - CORRECT
ANSWER✔✔y-90=1/38(x+5)
If the function is not differentiable at the given value of x, tell whether the problem is a corner,
cusp, vertical tangent, or a discontinuity
y= 4IxI+7, at x=0 - CORRECT ANSWER✔✔corner
If the function is not differentiable at the given value of x, tell whether the problem is a corner,
cusp, vertical tangent, or a discontinuity
y=(1)/(x-5), at x=5 - CORRECT ANSWER✔✔discontinuity (infinite)
If the function is not differentiable at the given value of x, tell whether the problem is a corner,
cusp, vertical tangent, or a discontinuity
y=9-cuberoot(x), at x=0 - CORRECT ANSWER✔✔vertical tangent
Determine the values of x for which the function is differentiable.
100% Correct Answers
Use the definition of f'(a)=lim h->0 of (f(a+h)-f(a))/(h) to find the derivative of the given function
at the indicated point
f(x)= 22-10x, a=1 - CORRECT ANSWER✔✔-10
Use the definition of f'(a)=lim h->0 of (f(a+h)-f(a))/(h) to find the derivative of the given function
at the indicated point
f(x)= x^3+7, a=4 - CORRECT ANSWER✔✔48
Use the definition of f'(a)=lim x->a of (f(x)-f(a))/(x-a) to find the derivative of the given function
at the indicated point
f(x)= √x, a=36 - CORRECT ANSWER✔✔1/12
Use the definition of f'(a)=lim x->a of (f(x)-f(a))/(x-a) to find the derivative of the given function
at the indicated point
f(x)= 4-x^2, a=8 - CORRECT ANSWER✔✔-16
Find dy/dx if y=17-4x - CORRECT ANSWER✔✔-4
Find d/dx(3x^2-2) - CORRECT ANSWER✔✔6x
, Find f'(x) if f(x)=8x-12 - CORRECT ANSWER✔✔8
Find an equation of the tangent line to the graph of y=x^2-x, at the point (3,6) - CORRECT
ANSWER✔✔y=5x-9
Find an equation of the tangent line to the graph of y=10√x-x+7 at the point (100,7) - CORRECT
ANSWER✔✔y-7=-1/2(x-100)
Find the equation of the normal line to the curve y=2x+4x^2 at the point (-5,90) - CORRECT
ANSWER✔✔y-90=1/38(x+5)
If the function is not differentiable at the given value of x, tell whether the problem is a corner,
cusp, vertical tangent, or a discontinuity
y= 4IxI+7, at x=0 - CORRECT ANSWER✔✔corner
If the function is not differentiable at the given value of x, tell whether the problem is a corner,
cusp, vertical tangent, or a discontinuity
y=(1)/(x-5), at x=5 - CORRECT ANSWER✔✔discontinuity (infinite)
If the function is not differentiable at the given value of x, tell whether the problem is a corner,
cusp, vertical tangent, or a discontinuity
y=9-cuberoot(x), at x=0 - CORRECT ANSWER✔✔vertical tangent
Determine the values of x for which the function is differentiable.
