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Let f: [a, b] → ℝ. Which of the following statement is/are true?
  • a)
    if f is continuous and injective, then f is monotone.
  • b)
    if f is differentiable and f'(x) ≠0 for all x∈ (a.b), then f is injective.
  • c)
    if f is differentiable and f'(a)<0< f'(b), then there is a c∈ (a,b) such that f'(c) = 0.
  • d)
    if f is differentiable and f'(a)<d <f '(b), then there is a c∈ (a.b) such that f'(c) = d
Correct answer is option 'A,B,C,D'. Can you explain this answer?
Most Upvoted Answer
Let f: [a, b] → . Which of the following statement is/are true?a)...
(c) & (d) follows from intermediate value theorem.
These are standard result and can be proved by contradiction.
All option are correct statement.
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Let f: [a, b] → . Which of the following statement is/are true?a)if f is continuous and injective, then f is monotone.b)if f is differentiable and f(x)≠0 for all x∈(a.b), then f is injective.c)if f is differentiable and f(a)<0< f(b), then there is a c∈(a,b) such that f(c) = 0.d)if f is differentiable and f(a)<d <f (b), then there is a c∈(a.b) such that f(c) = dCorrect answer is option 'A,B,C,D'. Can you explain this answer?
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Let f: [a, b] → . Which of the following statement is/are true?a)if f is continuous and injective, then f is monotone.b)if f is differentiable and f(x)≠0 for all x∈(a.b), then f is injective.c)if f is differentiable and f(a)<0< f(b), then there is a c∈(a,b) such that f(c) = 0.d)if f is differentiable and f(a)<d <f (b), then there is a c∈(a.b) such that f(c) = dCorrect answer is option 'A,B,C,D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let f: [a, b] → . Which of the following statement is/are true?a)if f is continuous and injective, then f is monotone.b)if f is differentiable and f(x)≠0 for all x∈(a.b), then f is injective.c)if f is differentiable and f(a)<0< f(b), then there is a c∈(a,b) such that f(c) = 0.d)if f is differentiable and f(a)<d <f (b), then there is a c∈(a.b) such that f(c) = dCorrect answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f: [a, b] → . Which of the following statement is/are true?a)if f is continuous and injective, then f is monotone.b)if f is differentiable and f(x)≠0 for all x∈(a.b), then f is injective.c)if f is differentiable and f(a)<0< f(b), then there is a c∈(a,b) such that f(c) = 0.d)if f is differentiable and f(a)<d <f (b), then there is a c∈(a.b) such that f(c) = dCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
Solutions for Let f: [a, b] → . Which of the following statement is/are true?a)if f is continuous and injective, then f is monotone.b)if f is differentiable and f(x)≠0 for all x∈(a.b), then f is injective.c)if f is differentiable and f(a)<0< f(b), then there is a c∈(a,b) such that f(c) = 0.d)if f is differentiable and f(a)<d <f (b), then there is a c∈(a.b) such that f(c) = dCorrect answer is option 'A,B,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
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