Find the equation of the tangent line to f(x)=6/x at x=-2

Step-by-step explanation:

Hey there! To find a tangent line of curve at specific point, we have to differentiate a given function. This is because a tangent line has same slope as the specific point and slope is equivalent to dy/dx.

From a given function, we can write as via law of exponent where .

Then differentiate with respect to x using power rules.

Power Rules

For every differentiatable continuous functions, if for u is any function and n is all real number.

Therefore:-

Therefore, our derived function is

Then substitute x = -2 in a derived function or slope.

Therefore, the slope at x = -2 is -3/2.

Now we have to use point-slope formula to find the equation of tangent line.

Point-Slope

We may have to find the (x,f(x)) coordinate first. We know x = -2 but we don’t know f(x) coordinate at x = -2 yet. We substitute x = -2 in f(x) to find f(-2).

Therefore, our coordinate is (-2,-3).

Substitute in point-slope form.

Then convert to slope-intercept form by isolating y-term and simplify the expression.

Therefore, the equation of tangent line is y = -3x/2.

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step-by-step explanation: