Cracking The Ap Calculus ab Exam 2018

expression by 3 and the numerator and the denominator of the bottom expression by 8. We get . Now, we can eva ...

Condition 2: f(x) exists. Condition 3: f(x) = f(c) Notice that the function is not defined at. Therefore, ...

4 x^3 We find the derivative of a function, f(x), using the definition of the derivative, which is f′(x) ...

We find the derivative of a function, f(x), using the definition of the derivative, which is f′(x) = . ...

(remember the shortcut that we showed you on this page). To find the derivative of , we first rewrite i ...

get f′(x) = . This can be simplified to f′(x) = . 22. 0 Here we will find the derivative using the ...

Recall that (cot x) = −csc^2 x. Here we use the Chain Rule to find the derivative: = (−csc^24 x)(4) ...

Factor out the term = sin x + cos x. Now, we can isolate , which can be simplified ...

by plugging x = 3 into the derivative of the equation. First, we find the y-coordinate, y 1 : y = ...

point (4, 7). Next, we take the derivative: = . Now, we can find the slope, m: = −6. How ...

slope, m: = −39. Finally, we plug in the point (5, −29) and the slope m = −39 to get the equation ...

is perpendicular to the tangent line, so its slope will be the negative reciprocal of the tangent line’s slop ...

(−1, 0) into the second equation, we get 0 = c(−1) + (−1)^2 , which simplifies to c = 1. Now we c ...

c = The Mean Value Theorem says that: If f(x) is continuous on the interval [a, b] and ...

endpoints) when doing Mean Value Theorem problems. If it is not, then the theorem does not apply. c ...

at both of the endpoints: f(1) = 1 − = 0 and f(−1) = 1 − = 0. Next, we take the deri ...

SOLUTIONS TO PRACTICE PROBLEM SET 10 The area is 32. First, let’s draw a picture. The rectangle can be e ...

negative answer doesn’t make any sense in the case, so we use the solution x = 2. We can then find the ...

this is a maximum by taking the second derivative: = −84 + 24x. Next, we plug in x = 1.697 to g ...

plug in x = 16 to get . Because the value of the second derivative is positive, according ...