Cracking The Ap Calculus ab Exam 2018

First, note that the derivative is zero at the point (0, 1) because the tangent line is horizontal there. ...

Note that it’s not important for your graph to be exact. All we are doing here is sketching the deriv ...

Notice that the tangent line looks as if it’s horizontal at x = 1. This means that the graph of ...

Here is an important one to understand. Suppose we have the graph of y = sin x. ...

Notice that the slope of the tangent line will be horizontal at all of the maxima and minima of the graph. B ...

First, notice that we have two vertical asymptotes at x = 6 and x = −6. This means that the grap ...

PRACTICE PROBLEM SET 6 Now try these problems. The answers are in Chapter 19. 1.Find if y = sin^2 x. 2.Find ...

6.Find if y = csc^2 x^2. 7.Find if y = sin 2x. 8.Find if y = sin t − cos t and t = 1 + ...

Chapter 7 Implicit Differentiation ...

HOW TO DO IT By now, it should be easy for you to take the derivative of an equation, such as y = 3 ...

A fraction that has the same term in its numerator and denominator is equal to 1, so we write = 2x ...

y^2 + y = 3x^5 − 7x You should use implicit differentiation any time you can’t write a function exp ...

After you factor out , divide both sides by 3y^2 − 8y. Note: Now that you understand that the derivati ...

Example 3: Find if 3x^2 + 5xy^2 − 4y^3 = 8. Implicit differentiation should result in the following ...

You need to use implicit differentiation to find . 6 x − 8 y = 0 Now, instead of rearranging to isolate ...

Now solve for . 2 − 10 = −12 − 1 2 = −3 SECOND DERIVATIVES Sometimes, you’ll be asked to find a s ...

Finally, substitute for . Try these solved problems without looking at the answers. Then check your work. ...

Grouping the terms, you get sin y − x = y − 1 Now factor out . (sin y − x) = y − 1 The derivative ...

Now substitute for and simplify. PRACTICE PROBLEM SET 7 Use implicit differentiation to find the following deri ...

8.Find if x^2 − 4x = 2 y − 2. ...