that returns a function: the derivative of a function f. Assuming that f is a single- variable mathematical function, its derivative will also be a single-variable function. When called with a number a, the derivative will estimate the slope of f at point (a, f(a)). Recall that the formula for finding the derivative of f at point a is: where h approaches 0. We will approximate the derivative by choosing a very small value for h. The closer h is to 0, the better the estimate of the derivative will be. def make_derivative (f): """Returns a function that approximates the derivative of f. >>> def square (x): f'(a) = lim h→0 Recall that f'(a) = (f(a+h)-f(a))/h as h approaches 0. We will approximate the derivative by choosing a very small value for h. ... ... f(a+h)-f(a) h #equivalent to: square = lambda x: X*X return x*x >>> derivative = make_derivative (square) >>> result = derivative (3) >>> round (result, 3) # approximately 2*3 6.0 Hu h=0.00001

that returns a function: the derivative of a function f. Assuming that f is a single- variable mathematical function, its derivative will also be a single-variable function. When called with a number a, the derivative will estimate the slope of f at point (a, f(a)). Recall that the formula for finding the derivative of f at point a is: where h approaches 0. We will approximate the derivative by choosing a very small value for h. The closer h is to 0, the better the estimate of the derivative will be. def make_derivative (f): """Returns a function that approximates the derivative of f. >>> def square (x): f'(a) = lim h→0 Recall that f'(a) = (f(a+h)-f(a))/h as h approaches 0. We will approximate the derivative by choosing a very small value for h. ... ... f(a+h)-f(a) h #equivalent to: square = lambda x: XX return xx >>> derivative = make_derivative (square) >>> result = derivative (3) >>> round (result, 3) # approximately 2*3 6.0 Hu h=0.00001

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Define a function make_derivative that returns a function: the derivative of a function f. Assuming that f is a single-
variable mathematical function, its derivative will also be a single-variable function. When called with a number a,
derivative will estimate the slope of f at point (a, f(a)).
the
Recall that the formula for finding the derivative of f at point a is:
f'(a) = lim
h→0
where h approaches 0. We will approximate the derivative by choosing a very small value for h. The closer h is to 0, the
better the estimate of the derivative will be.
def make_derivative (f):
"""Returns a function that approximates the derivative of f.
>>> def square (x):
f(a+h)-f(a)
h
Recall that f'(a) = (f(a + h) - f(a)) / h as h approaches 0. We will
approximate the derivative by choosing a very small value for h.
# equivalent to: square = lambda x: x*X
return x*x
>>> derivative = make_derivative (square)
>>> result = derivative (3)
>>> round (result, 3) # approximately 2*3
6.0
||||||
h=0.00001
"*** YOUR CODE HERE ***"

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