graph is f(x) 2^x 1.++-1123.a. Use the graph to explain why, for h > 0,f(a – h) – f(a)-hf(a + h) – f(a)< f'(a) <h

The formula for f’(x) for f(x) = 2x is given asddxax=axlnaif a=2 then:ddx2x=2xln2f'x=2xln2

Answered: 1. + + -1 1 2 3. a. Use the graph to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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graph is f(x) 2^x

1.
+
+
-1
1
2
3.
a. Use the graph to explain why, for h > 0,
f(a – h) – f(a)
-h
f(a + h) – f(a)
< f'(a) <
h

Expert Solution

Step 1

The formula for f’(x) for f(x) = 2^xis given as $\frac{d}{d x} (a^{x}) = a^{x} \ln (a) i f a = 2 t h e n : \frac{d}{d x} (2^{x}) = 2^{x} \ln (2) f' (x) = 2^{x} \ln (2)$

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