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Solution for State When a Function F(X) is Said to Be Increasing on an Interval [A, B]. Test Whether the Function F(X) = X2 − 6x + 3 is Increasing on the Interval [4, 6] ? - CBSE (Science) Class 12 - Mathematics

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Question

State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?

Solution

\[\text { A function f(x) is said to be increasing on } \left[ a, b \right] \text { if it is increasing at  x = a and x = b } . \]

\[\text { Here, } \]

\[f\left( x \right) = x^2 - 6x + 3\]

\[f'\left( x \right) = 2x - 6\]

\[ \Rightarrow f'\left( x \right) = 2\left( x - 3 \right)\]

\[\text { Now, } f'\left( 4 \right) = 2\left( 4 - 3 \right)\]

\[ = 2\]

\[ \therefore f'\left( 4 \right) > 0 \]

\[\text { So, f(x) is increasing on x}  = 4 \]

\[\text { &, }f'\left( 6 \right) = 2\left( 6 - 3 \right)\]

\[ = 6\]

\[ \therefore f'\left( 6 \right) > 0 \]

\[\text { So, f (x) is increasing on x } = 6 \]

\[\text { Hence,}f\left( x \right)\text { is increasing on } [4, 6].\]

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Solution for question: State When a Function F(X) is Said to Be Increasing on an Interval [A, B]. Test Whether the Function F(X) = X2 − 6x + 3 is Increasing on the Interval [4, 6] ? concept: Increasing and Decreasing Functions. For the courses CBSE (Science), CBSE (Commerce), PUC Karnataka Science, CBSE (Arts)
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