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 Equation of the tangent is Refer the graph Watch the video alsoenter link description here
The slope of the tangent is -14
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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.
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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