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The function $f(x) = 3 + 2x + 32x^{-1}$ has one local minimum and one local maximum. This function has a local maximum at $x =$ with value and a local minimum at $x =$ with value

          The function $f(x) = 3 + 2x + 32x^{-1}$ has one local minimum and one local maximum.
This function has a local maximum at $x =$
with value
and a local minimum at $x =$
with value
        
The function f(x) = 3 + 2x + 32x^-1 has one local minimum and one local maximum.
This function has a local maximum at x =
with value
and a local minimum at x =
with value

Added by Jennifer T.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The function f(x)=3+2x+32x^(-1) has one local minimum and one local maximum. This function has a local maximum at x= with value and a local minimum at x= with value The function f() = 3 + 2 + 32-1 has one local minimum and one local maximum. This function has a local maximum at = with value and a local minimum at= with value
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Transcript

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00:03 Here, given f of x is equal to 2 plus 7x plus 63 upon x.
00:09 Name it equation 1.
00:12 Now we have to find out the local maximum and local minimum point.
00:19 So differentiating equation 1 with respect to x, we get f dash x is equal to 7 minus 63 upon x square.
00:33 Now in order to find out the local maximum or local minimum, using the formula f dash x is equal to 0, we get 7 minus 63 upon x square is equal to 0, which implies 7x square is equal to 63, which implies x square is equal to 9, which implies x is equal to plus minus 3.
01:03 So at x is equal to 3, we have to find out f double dash 3.
01:12 So again differentiating equation 1 twice with respect to x, we get f double dash x is equal to 63 multiplied by 2 upon x cube, which is equal to 126 upon x cube.
01:44 Therefore, f double dash 3 is 4 .7, which is greater than 0.
01:56 Hence, at x is equal to 3, local minimum is attained.
02:14 Now, the other value that is x is equal to minus 3, we have to evaluate f double dash minus 3...
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