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Oct 1, 2024 · Solution: The slope of a tangent line can be found by finding the derivative of the curve f (x and finding the value of the derivative at the point where the tangent line and the curve meet. This gives us the slope. For example: Find the slope of the tangent line to the curve f (x) = x² at the point (1, 2).
AI explanations are generated using OpenAI technology. AI generated content may present inaccurate or offensive content that does not represent Symbolab's view. slope\:of\:tangent\:f (x)=\sin (2x),\:x=\frac {\pi} {2} Find the slope of the tangent line given a point or the intercept step-by-step. Ski Vacation?
If y = f(x) is the equation of the curve, then f'(x) will be its slope. So, slope of the tangent is m = f'(x) or dy/dx. Let us look into some examples to understand the above concept. Example 1 : Find the equation of the slope of tangent to the parabola y 2 = 12x at the point (3, 6) Solution : Equation of the given curve is y 2 = 12x. 2y (dy/dx ...
Possible Answers: Correct answer: Explanation: One way of finding the slope at a given point is by finding the derivative. In this case, we can take the derivative of y with respect to x, and plug in the desired value for x. Using the exponential rule we get the following derivative, . Plugging in x=2 from the point 2,3 gives us the final slope,
The tangent line of a curve y = f(x) is a line that touches the curve at a point (x 0, y 0). Its slope (m) is found by substituting the point where it is drawn in the derivative f'(x) and its equation is found by using y - y 0 = m (x - x 0). How to Find the Slope of a Tangent Line? The slope of a tangent line at a point is its derivative at ...
The tangent line to a curve at a given point is a straight line that just "touches" the curve at that point. So if the function is f (x) and if the tangent "touches" its curve at x=c, then the tangent will pass through the point (c,f (c)). The slope of this tangent line is f' (c) ( the derivative of the function f (x) at x=c).
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contributed. The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point. Finding the tangent line to a point on a curved graph is challenging and requires the use of calculus; specifically, we will use the derivative to find the slope of the curve.
