Question:medium
Let $f(x)=x^{2}-10x+16$, $x\in\mathbb{R}.$ If $f^{\prime}(c)$ is equal to slope of the straight line joining the points (2,0) and (8,0), then the value of $c$ is
Let $f(x)=x^{2}-10x+16$, $x\in\mathbb{R}.$ If $f^{\prime}(c)$ is equal to slope of the straight line joining the points (2,0) and (8,0), then the value of $c$ is
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Logic Tip: A powerful shortcut for ANY quadratic function $f(x) = ax^2+bx+c$: The point $c$ where the tangent is parallel to the secant line between $x_1$ and $x_2$ is EXACTLY the midpoint. $c = \frac{x_1 + x_2}{2}$. Here, $\frac{2 + 8}{2} = 5$. No calculus required!
Updated On: Apr 27, 2026
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The Correct Option is D
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