Find the slope of the curve y = 1/x at any point x = a, a neq 0. What | Basic Mathematics 0

Basic Mathematics05 marksNumerical: slope of curveDerivative as slope of tangent line

Find the slope of the curve $y = 1/x$ at any point $x = a$ , $a \neq 0$ . What is the slope at the point $x = -1$ ? Where does the slope equal $-1/4$ ? What happens to the tangent to the curve at the point $(a, 1/a)$ as $a$ changes? [2+1.5+1.5]

Find the slope of the curve $y = 1/x$ at any point $x = a$, $a \neq 0$. What is the slope at the point $x = -1$? Where does the slope equal $-1/4$? What happens to the tangent to the curve at the point $(a, 1/a)$ as $a$ changes? [2+1.5+1.5]

Curve: $y = \dfrac{1}{x}$ - Point of interest: $x = a$ , with $a \neq 0$ - Specific values to evaluate: slope at $x = -1$ ; where slope $= -\dfrac{1}{4}$ ; behavior of tangent at $(a, 1/a)$ as $a$ varies --- Write $y = x^{-1}$ . Differentiating using the power rule: $$\frac{dy}{dx} = -1 \cdot x^{-2...

Curve: $y = \dfrac{1}{x}$ - Point of interest: $x = a$, with $a \neq 0$ - Specific values to evaluate: slope at $x = -1$; where slope $= -\dfrac{1}{4}$; behavior of tangent at $(a, 1/a)$ as $a$ varies --- Write $y = x^{-1}$. Differentiating using the power rule: $$\frac{dy}{dx} = -1 \cdot x^{-2...

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Find the slope of the curve y = 1/x at any point x = a, a neq 0. What is the slope at the point x = -1? Where does the slope equal -1/4? What happens to the tangent to the curve at the point (a, 1/a) as a changes? [2+1.5+1.5]