Show that the function given by f(x) = e^2x is strictly increasing on R.

Solution

Here f (x) = e^{2 x} ⇒ f ' (x) = 2 e^2xThree cases arise:
Case I.
$straight x space greater than 0$
$Syntax error from line 1 column 565 to line 1 column 668. Unexpected '<mlongdiv '.$
Case II. x = 0
$therefore space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 2 straight e to the power of 0 space equals space 2 space straight x space 1 space equals space 2 space greater than space 0$
Case III,
$straight x less than 0$
$therefore space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 2 straight e to the power of 2 straight x end exponent space equals space 2 over straight e to the power of negative 2 straight x end exponent space equals space fraction numerator 2 over denominator space straight a space positive space quantity end fraction greater than 0 therefore space space space space in space all space the space three space cases comma space space space straight f apostrophe left parenthesis straight x right parenthesis space greater than space 0 therefore space space space space straight f left parenthesis straight x right parenthesis space equals space straight e to the power of 2 straight x end exponent space is space strictly space increasing space on space straight R.$

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Application Of Derivatives

Show that the function given by f(x) = e^2x is strictly increasing on R.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Show that the function given by f(x) = e2x is strictly increasing on R.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Show that the function given by f(x) = e^2x is strictly increasing on R.