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The tangent to the curve y = ex drawn at the point (c, ec) intersects the line joining the points (c – 1, ec–1) and (c + 1, ec + 1)
  • a)
    on the left of x = c
  • b)
    on the right of x = c
  • c)
    at no point
  • d)
    at all points
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The tangent to the curve y = ex drawn at the point (c, ec) intersects ...
The equation of tangent to the curve y = ex at (c, ec) is
y - ec = ec (x-c) … (1)
and equation of line joining (c –1, ec–1) and (c +1, ec+1) is

Subtracting equation (1) from (2), we get

∴ The two lines meet on the left of line x = c.
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Most Upvoted Answer
The tangent to the curve y = ex drawn at the point (c, ec) intersects ...
To find the equation of the tangent to the curve y = ex at the point (c, ec), we need to find the slope of the tangent line at that point.

The slope of the tangent line is equal to the derivative of the function y = ex evaluated at x = c.

Taking the derivative of y = ex, we get:

dy/dx = ex

Evaluating this derivative at x = c, we get:

dy/dx = ec

So the slope of the tangent line is ec.

Now, we need to find the equation of the line that passes through the points (c, ec) and (c+1, ec+1).

The slope of the line passing through these two points is given by:

m = (ec+1 - ec) / (c+1 - c) = ec+1 - ec

So the equation of the line is:

y - ec = (ec+1 - ec)(x - c)

Simplifying this equation, we get:

y = (ec+1 - ec)x + ec - (ec+1 - ec)c

y = (ec+1 - ec)x + ec - ec

y = (ec+1 - ec)x

Therefore, the equation of the tangent line to the curve y = ex at the point (c, ec) is:

y = (ec+1 - ec)x.
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The tangent to the curve y = ex drawn at the point (c, ec) intersects the line joining the points (c – 1, ec–1) and (c + 1, ec + 1)a)on the left of x = cb)on the right of x = cc)at no pointd)at all pointsCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The tangent to the curve y = ex drawn at the point (c, ec) intersects the line joining the points (c – 1, ec–1) and (c + 1, ec + 1)a)on the left of x = cb)on the right of x = cc)at no pointd)at all pointsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The tangent to the curve y = ex drawn at the point (c, ec) intersects the line joining the points (c – 1, ec–1) and (c + 1, ec + 1)a)on the left of x = cb)on the right of x = cc)at no pointd)at all pointsCorrect answer is option 'A'. Can you explain this answer?.
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