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Chapter 2: Q 3. (page 237)

Translate expressions written in Leibniz notation to 鈥減rime鈥� notation, and vice versa.

f''(x)

Short Answer

Expert verified

f''(x)=d2fdx2

Step by step solution

01

Given Information

The given expression isf''(x)

02

Simplification

f''(x)is written in prime notation.

It means double differentiation of function w.r.t x

In Leibnitz notation,f''(x)=d2fdx2

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Most popular questions from this chapter

Prove that if f is any cubic polynomial function f(x)=ax3+bx2+cx+dthen the coefficients of f are completely determined by the values of f(x) and its derivative at x=0 as follows

a=f"'(0)6;b=f"(0)2;c=f'(0);d=f(0)

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=1+x23x2-4x+1

For each function f(x)and interval a,bin Exercises 81-86, use the Intermediate Value Theorem to argue that the function must have at least one real root on a,b. Then apply Newton鈥檚 method to approximate that root.

f(x)=x3+1,a,b=-2,1

Each graph in Exercises 31鈥�34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The tangent line to f(x)=x2 atx=0
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