TS EAMCET · Maths · Application of Derivatives
If \(f:[a, b] \rightarrow[c, d]\) is a continuous and strictly increasing function, then \(\frac{d-c}{b-a}\) is
- A Value of the function at a point \(t \in(a, b)\)
- B Value of the function at \(t \in(a, b)\) such that \(f^{\prime}(t)=0\)
- C Slope of the tangent drawn to the curve \(y=f(t)\) at a point \(t \in(c, d)\)
- D Slope of the tangent drawn to the curve \(y=f(t)\) at a point \(t \in(a, b)\)
Answer & Solution
Correct Answer
(D) Slope of the tangent drawn to the curve \(y=f(t)\) at a point \(t \in(a, b)\)
Step-by-step Solution
Detailed explanation
\(f(a)=c, f(b)=d\) \(\frac{d-c}{b-a} = \frac{f(b)-f(a)}{b-a}\) By Mean Value Theorem, there exists \(t \in (a, b)\) s.t. \(\frac{f(b)-f(a)}{b-a} = f'(t)\). This is the slope of the tangent drawn to the curve \(y=f(t)\) at a point \(t \in (a, b)\).
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