Need help with derivative question

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In summary, the question is to determine the values of a and b for the curve y=ae2x + bx, where the tangent at point (0,4) has a gradient of 3. The solution involves differentiating the curve and using the given information to create a system of equations to solve for a and b.
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linapril
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I've solved half the question (I think), but then gotten stuck... Can someone help me out?

The question:
The tangent to the curve y=ae2x + bx on the point (0,4) has the gradient k=3. Determine the values of a and b.

My solution:
y' = 2ae2x+b
y'(0) = 3
2ae2(0)+b)=3
2a+b=3
b=3-2a

And this is where I don't know how to proceed...
Would appreciate some help!
 
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  • #2
You have correctly done the hard part of differentiation. (Sun)

You also know $y(0)=4$. This will give you a second equation in the two unknowns, and then you will be able to determine the solution.
 

FAQ: Need help with derivative question

What is a derivative?

A derivative is a mathematical tool used to measure the rate of change of a function with respect to its input variable. It is the slope of the tangent line to the function at a specific point.

How do I find the derivative of a function?

To find the derivative of a function, you can use the rules of differentiation such as the power rule, product rule, quotient rule, and chain rule. These rules allow you to find the derivative of any function by breaking it down into simpler parts and applying the rules accordingly.

Why is finding the derivative important?

Finding the derivative of a function is important because it allows us to understand the behavior of a function and its rate of change. It is used in many areas of mathematics, physics, engineering, and economics to solve problems involving rates of change, optimization, and approximation.

What is the difference between a derivative and an antiderivative?

A derivative measures the rate of change of a function, while an antiderivative is the inverse operation of differentiation and represents the original function before it was differentiated. In other words, the derivative of a function gives its slope, while the antiderivative gives the area under the curve.

How can I use derivatives to solve real-world problems?

Derivatives can be used to solve a variety of real-world problems such as finding maximum and minimum values, determining rates of change, and optimizing functions. For example, derivatives can be used to find the maximum profit for a business or the fastest route for a car to take in a race.

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