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(D) According to the Mean Value Theorem $(MVT)$,if a function $f$ is continuous on $[a, b]$ and differentiable on $(a, b)$,there exists at least one p

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Slope of the tangent drawn to the curve $y = f(t)$ at a point $t \in (a, b)$

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(D) According to the Mean Value Theorem $(MVT)$,if a function $f$ is continuous on $[a, b]$ and differentiable on $(a, b)$,there exists at least one point $t \in (a, b)$ such that $f^{\prime}(t) = \frac{f(b) - f(a)}{b - a}$.Since $f$ is a strictly increasing function from $[a, b]$ to $[c, d]$,we have $f(a) = c$ and $f(b) = d$.Substituting these values into the $MVT$ formula,we get $f^{\prime}(t) = \frac{d - c}{b - a}$.Therefore,$\frac{d - c}{b - a}$ represents the slope of the tangent to the curve $y = f(t)$ at some point $t \in (a, b)$.

If $f:[a, b] \rightarrow [c, d]$ is a continuous and strictly increasing function,then $\frac{d-c}{b-a}$ is

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