Local extreme value

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ashil

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Suppose f is differentiable on -infinity and +infinity(everywhere) and assume that it has a local extreme value at the point (2,0). Let g(x)=xf(x)+1 and h(x)=xf(x)+x+1 for all values of x.
Evaluate g(2), h(2), g'(2) and h'(2).


g(2) = xf(x)+1
since x = 2, f(2) = 0
g(2) = 2(0)+1
= 1


h(2) = xf(x)+x+1
= 2(0) + 2 + 1
= 3


can you please check the to equations that i have solved and can you please help me with g'(2) and h'(2).
 
ashil said:
Suppose f is differentiable on -infinity and +infinity(everywhere) and assume that it has a local extreme value at the point (2,0). Let g(x)=xf(x)+1 and h(x)=xf(x)+x+1 for all values of x.
Evaluate g(2), h(2), g'(2) and h'(2).


g(2) = xf(x)+1
since x = 2, f(2) = 0
g(2) = 2(0)+1
= 1


h(2) = xf(x)+x+1
= 2(0) + 2 + 1
= 3
Looks good!

can you please check the to equations that i have solved and can you please help me with g'(2) and h'(2).
Click to expand...

1. You know that at (2, 0) there is a local extremum. What do you know then about f'(2) ?

2. Differentiate g using product rule:

\(\displaystyle g(x)=x f(x) +1\)

\(\displaystyle g'(x)=f(x) \cdot 1 + x \cdot f'(x)\)

Since you know the values of f(x), f'(x) and x you can determine g'(2).

3. The question concerning the function h should be done in a similar way.
 
Looks like possible classmates; respective locations are ~8 mi apart.
 
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