Linear Approximation 2

Computer Science Level 3

This is sequence to my previous problem .

Make sure you attempt it first to get familiar with the terms.

Approx the value of $f(4)$ using step size of $0.2$ , given you know the following regard a function $f$ -

$f(2) = 4$

and

$f'(x) = 2 \times x - 7$

Round off your answer to $2$ decimal digits.

For example, if your answer is $1.4567$ you should write it as $1.46$ .

Good Luck!

The answer is 1.6.

1 solution

Lokesh Sharma
Apr 1, 2014

Python Solution:

def dervf(x):
    '''
    Returns derviative of f at x
    '''
    return 2*x - 7

def linearApprox_helper(a, fa, step):
    '''
    Given value of f at any point a,
    it approximates the value of f at a + step
    '''
    return fa + step * dervf(a)

def linearApprox(stop, step):
    '''
    Approx value of f(stop)
    given the value the step size as step
    '''
    a = 2 # start value = 2
    fa = 4 # equivalent to f(a) = 4
    while a < stop:
        fa = linearApprox_helper(a, fa, step)
        a += step
    return fa

print linearApprox(4, 0.2)

I also solved using Microsoft Excel :)

Rhoy Omega - 6 years, 4 months ago

Linear Approximation 2

The answer is 1.6.

1 solution

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