Question

Suppose g (x) is increasing and concave up everywhere and g(A)=7, gprime(A)=13, h=.01
Estimate g(A-h) and g(A+h).

Answer 1

The required values are,

$g(A-h)=6.87$

$g(A+h)=7.13$

Concave up and Concave down:

What Do “Concave Up” and “Concave Down” Mean? Concave up (also called convex) or concave down are descriptions for a graph, or part of a graph: A concave up graph looks roughly like the letter U; A concave down graph is shaped like an upside-down U. They tell us something about the shape of a graph, or more specifically, how it bends.

Given that,

$g\left( A \right)=7, \ g'\left( A \right)=13$

$h=0.01$

$g'\left( A \right)\approx \frac{g\left( A-h \right)-g\left( A \right)}{h}\\\Rightarrow g\left( A \right)-g\left( A-h \right)\approx hg'\left( A \right)\\=7-(0.01)(13)\\=6.87$

we use the formula,

$g'\left( A \right)\approx \frac{g\left( A+h \right)-g\left( A \right)}{h}\\\Rightarrow g\left( A+h \right)\approx hg'\left( A \right)+g\left( A \right)\\=(0.01)(13)+7\\=7.13$

Learn more about the topic concave up and concave:

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