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Estimate f(4.04) for f as in the figure

Estimate f(4.04) for f as in the figure-example-1
User Ravuya
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7.2k points

2 Answers

5 votes

Answer:

2.013 to 3 DP's.

Explanation:

f(4.04) will be very close to the tangent line.

Equation of tangent line

is y - 4 = m(x - 10)

m = (4-2) / (10-4) = 1/3

y - 4 = 1/3(x - 10)

y = 1/3x - 10/3 + 4

y = 1/3x + 2/3

So the require estimate of f(4.04)

= 1/3(4.04) + 2/3

= 2.013333

User FriendOfFuture
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6.5k points
2 votes

Estimate value f(4.04)≈2.941

To estimate f(4.04), we refer to the given figure, which includes a function f(x) plotted on a coordinate plane. The point (4, 2) lies on the curve of the function, and a tangent line to the curve at this point is shown. Using this information, we can approximate the value of f(4.04).

The tangent line at (4, 2) provides an approximation of the function's behavior near this point. To estimate f(4.04), we consider the corresponding y-value on the tangent line. The figure does not provide an exact value, but it appears to be approximately 2.941 based on the graph.

Therefore, f(4.04) is estimated to be approximately 2.941, rounded to three decimal places. This estimation is derived from the tangent line's slope at the given point on the curve.

User Tibincrunch
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6.7k points