# How do you find the equation of the line tangent to the graph of #f(x) = 6 - x^2# at x = 7?

Given -

It is a quadratic function.

Since co-efficient of

The slope of the curve at any given point is its 1st erivative.

At

At

The slope of the tangent is -14

Equation of the tangent is

Refer the graph

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To find the equation of the line tangent to the graph of f(x) = 6 - x^2 at x = 7, we need to find the derivative of the function f(x) and evaluate it at x = 7. The derivative of f(x) is f'(x) = -2x. Evaluating f'(x) at x = 7, we get f'(7) = -2(7) = -14.

The slope of the tangent line is equal to the derivative of the function at the given point, so the slope of the tangent line is -14.

To find the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values x1 = 7, y1 = f(7) = 6 - (7^2) = -43, and m = -14, we have y - (-43) = -14(x - 7). Simplifying this equation gives the equation of the tangent line as y = -14x + 85.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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