Cracking The Ap Calculus ab Exam 2018

derivative is positive. Therefore, according to the second derivative test (see this page), the perimeter ...

that the swimmer needs. The time for the swimmer to travel D 1 is T 1 = (because she ...

We need to find an expression for the distance from the point P to the point (2, 1) and then minimize ...

Next, we can simplify and square both sides: x^2 = 4(1 − x^2 ). Now, we can solve this easily. We g ...

is 2r + 2h + πr = 288. We can use the equation for the perimeter to eliminate a variable from the equ ...

expression into the area formula. First isolate y = , then plug in: A = x^2 + 4x = x^2 ...

and at x = − y′ = . This is the larger of the two, so the maximum slope is at x = − . Now we ju ...

Minimum at (−3, −4); Maximum at (−1, 0); Point of inflection at (−2, −2). First, let’s find the ...

we plug x = −1 into the second derivative, the value is negative, so (−1, 0) is a maximum. If we p ...

get y = −x^4 + 13x^2 − 36. Now we can take the derivative: = −4x^3 + 26x. Next, we set the deri ...

second derivative, the value is negative, so is a maximum. If we plug x = − into the second deriva ...

derivative: . If we set this equal to zero, there is also no solution. Therefore, there are no maxim ...

Vertical asymptote at x = 3; Oblique asymptote of y = x + 3; Maximum at (3 + , 6 + 2 ); Minimum ...

vertical asymptote at x = 3. There is no horizontal asymptote, but notice that the degree of the numerato ...

Now, we can draw the curve. It looks like the following: No maxima, minima, or points of inflection; Cusp ...

function has either a vertical tangent or a cusp at x = 0. We’ll be able to determine which afte ...

Maximum at (1, 1); No point of inflection; Cusp at (0, 0). First, we notice that the curve has x-intercepts ...

− − 2. Next, we set the derivative equal to zero to find the critical points. There is one ...

SOLUTIONS TO PRACTICE PROBLEM SET 12 2,000 ft^2 /s We are given the rate at which the circumference is in ...

A = πr^2 . We could find C in terms of r and then plug it into the equation for A, or we coul ...