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Find the equation of the tangent line to y = 2^(x² - 5x + 3) at x = 4.

User Septi
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1 Answer

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Final answer:

To find the equation of the tangent line, we need to find the derivative of the function and evaluate it at the given point. Then, we can use the point-slope form of a line to find the equation of the tangent line.

Step-by-step explanation:

To find the equation of the tangent line, we first need to find the derivative of the function y = 2^(x² - 5x + 3). Using the power rule and chain rule, the derivative is given by dy/dx = 2^(x² - 5x + 3) * (2x - 5 * ln(2)). Evaluating this derivative at x = 4, we can find the slope of the tangent line. Substituting the values into the derivative, we get dy/dx = 2^(4² - 5 * 4 + 3) * (2 * 4 - 5 * ln(2)). This gives us the slope of the tangent line at x = 4.

Next, we can use the point-slope form of a line, y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. We substitute the values x = 4 and m = dy/dx into the equation to find the equation of the tangent line.

Therefore, the equation of the tangent line to y = 2^(x² - 5x + 3) at x = 4 is given by y - y₁ = dy/dx(x - x₁). Substitute the values and simplify to get the final equation of the tangent line.

User Steen Harsted
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